Mathematicians brag about their Erdös number[1]. Go players can brag about their Shusaku number. This
is the smallest number of games that link you to Shusaku.
More explicitly, it is the first number
in the following list which applies to you:
0. You are Shusaku (Shusaku has number 0).
1. You have played Shusaku.
2. You have played someone who has played Shusaku.
N+1. You have played someone with Shusaku number N.
Infinity. If there is no sequence of games linking you to Shusaku, your number is infinite. [2]
Note: A sequence of games linking you to Shusaku only gives an an upper bound. In order to state your exact Shusaku number, you have to show that no shorter sequence exists.
(If you've played a few dozen games online among disparate players, your ShusakuNumber is probably finite. If your ShusakuNumber is finite, it's almost certainly less than 10.)
What's your Shusaku number?
Like a Six Degrees of Separation for Go... interesting.
If you ever had the honour of playing against Iwamoto Sensei it is at most 4. Based on games in GoGod (except the last one :))
I didn't have that honour! But I still get a 5:
Dave Sigaty: There are probably better bridges than "Shusai --> XX". Iwasaki Kenzo died in 1913, Shuei died in 1907, Shugen died in 1917. Although they were too young to play any official games both Shuei and Shugen were sons of Shuwa and most likely knew Shusaku. There is an excellent chance that they played him as children. People like Segoe (d. 1972), Iwamoto (d. 1999), Hayashi Yutaro (d. 1983) directly spanned the gap between the beginning of the century and modern times.
Bob McGuigan: My number is at most 4 via an unusual path in that two of the players are female: Bob--Shiratori Sumiko--Kita Fumiko--Shuho--Shusaku.
Jared Beck: I also use the Shiratori Bridge:
Anyone who has played the user "breakfast" on KGS has a Shusaku Number of 6.
Bob McGuigan: It's interesting to speculate on who wouldn't have a Shusaku number. I'm sure there are such people. For example two people who "found" go in a game shop, bought a set, learned the rules from the enclosed pamphlet, and have only played each other. On the other hand, anyone who's ever played anyone who has ever played ...(iterate ad libitum) ... anyone who has ever played any pro, even in a simultaneous game, would have a Shusaku number (I'm sure the pros are all connected to Shusaku).
Shuei played Shuho providing additional "bridge" to Shusaku. Shuei, who died 1907, may provide a better bridge than Shuwa, who died in 1873. KariganeJunichi died in 1953, late enough to have played many of todays more senior professionals.
Bob McGuigan: Shuwa's number is 1.
The earliest opponents recorded on http://www.GoBase.org
for Hayashi Yutaro (3) are Shusai, Kitani Minoru and Go Seigen. So, Hayashi Yutaro may not be a better 'bridge' to Shusaku.
Iwamoto's (3) connection to Shusaku suffers the same problem
per http://www.GoBase.org. Iwamoto (3) connects via Shusai, Kitani Minoru and Go Seigen as well.
Velobici: Could someone with a copy of GoGoD or Master Go check for better links to Shusaku?
Dave Sigaty: The games in the databases from the early 20th century come from a limited number of books (e.g. Igo Hyakunen) plus a few published game collections such as Shusai, Go, Kintani, and Hashimoto Utaro. This limits what we can demonstrate from the readily available sources, but realize that there are huge gaps in the information.
Jan van Rongen: I tried the other connections too, but they all run into some problems. Of course there is the formal problem of the availability of a game record. On the other hand Iwamoto is very unlikely to have a lower Shusaku number. He did not arrive in Japan until 1911 and reached Sho-dan in 1917. Segoe moved to Tokyo when he was 20 (1908) where he was promoted to 2 dan in the end of that year. So he might have played against Iwasaki or Shugen. Which would give all his pupils Shusaku number (3), including Cho Hun-hyeon. But again -- we need the game records to be sure.
MtnViewMark: Do we count teaching games or only games played to win?
A refinement of the idea would be your Winning Shusaku Number: which is one greater than the least Winning Shusaku Number of all the people you've ever defeated (at an even game, say).
Stefan: How do deshi feel about Shindo Hikaru as a bridge? He has played Shusaku's Go engine on multiple occasion, and therefore carries a 1. The problem probably is to find a game between Shindo and somebody with us here in meatspace.
BlueWyvern: How would you define meatspace? (BTW, Maybe Umezawa Yukari has a Shusaku # of 2)
Jared: Meatspace is a term from Gibson's novel Neuromancer, and refers to real life, the opposite of cyberspace.
[1] The practice for Erdös numbers is that Paul Erdös has uniquely the Erdös number 0. Then everybody else has Erdös number defined to be one greater than the minimum of their co-authors' Erdös numbers. As in graph theory the reflexive edges are discarded: one does not consider either the papers under Erdös' single authorship or, analogously, Shusaku's solitaire games.
MrMoto: To clarify the mechanics of the Erdös number:
Let G be a graph with vertices labeled by people. Vertices P and Q are adjacent if and only if P and Q have co-authored a paper. Then the Erdös number of person P is the distance from P to Erdös.
Fwiffo: Both Erdös numbers and Bacon numbers are based on the work of Stanley Milgram which inspired the book and movie "Six Degrees of Separation".
Rafael Caetano: Really? Erdös and many of his colleagues studied graph theory. It would be surprising if they had to see Milgram's work to come up with the idea of a collaboration graph.
ilan: The co-author graph is actually a hypergraph. In fact, you can take the general co-authors + papers situation as a definition of hypergraph. The "six degrees of separation" hypothesis alluded to above is that any two people in the world can be linked by a chain of 6 people where any two consecutive members of the chain have met each other. Mathematically, I believe that this can be interpreted as follows: the diameter of a random hypergraph is of the order of the logarithm of the number of vertices.
I've been told that Paul Erdös enjoyed playing go -- in fact, that it was his only hobby aside from visiting other mathematicians. Can anyone corroborate this? Any idea how strong a player he was? Do we have any readers with a Erdös Go number of 1 (played a game of go with Paul Erdös)?
Charles Matthews: Yes, I played him twice. The first time was probably around 1975. He was around 2 kyu then. I played him a few years later, and he was perhaps a little stronger; but given his habits that might not be significant. There is even a photo I've seen of him playing, in an AMS publication - sadly he was in hane at the head of three bad shape there.
Matt Noonan: In Budapest there is an annual Erdös Pal Go tournament (as of 2001). Too bad he can't make it...
enel: Unfortunately my Erdős Go Number is 2 only (Erdős-Göndör-enel). I saw him sometimes while he playing in Budapest. He has a "famous" saying related to the go game. "May play go wrong, but must not play slow". Erdős played very quickly.
Chad Miller: I wonder what Erdős' ShusakuNumber was.
Evand: I'd be interested in knowing James Kerwin's Shusaku number. Is it low enough to provide a useful bridge? If someone with a database could look into it, I'd find it interesting. Thanks.
BobMcGuigan: Kerwin was a student of Iwamoto (see above) so he probably played at least one game with him.
Velobici: James Kerwin has a Shusaku number that is not greater than 4: Shusaku - Iwasaki Kenzo - Honinbo Shusai - Iwamoto Kaoru - James Kerwin.
FFLaguna: DrStraw has a Shuusaku number of 4 and a Go Seigen number of 2! Convo him for a game, or some such! ^.^
Crimson: If I have an infinite shusaku number, and I play someone which also has an infinite shusaku number, and after the game he gets a finite number, do I get a number too?
And what if I have, say, number 6: Shusaku < X < Y < Z < W < T < me, and then T plays Z, does my number decrease?
Crimson : Thanks
Bildstein : That's a bit disappointing. I liked the idea that something, even though it be intangible, could pass from player to player, so that a Shusaku Number could have some meaning, though it be intangible. But this is simply not the case if the answers to Crimson's questions are 'Yes'. If I, as a 28 kyu, play a few games against a friend of mine, also a 28 kyu, and then a few years later he's reached professional level and I haven't improved at all, and then he moves to Japan and plays against Shusaku himself, I certainly won't feel like I have a Shusaku Number of 2. I will feel like I still don't have a Shusaku Number.
[2] Bildstein: It doesn't make sense to talk about having a Shusaku Number of infinity. Having a Shusaku Number number of N means at least N games have been played between at least N + 1 players, but there is no infinite list of games between an infinite number of players you can present to justify your claim of having an infinite Shusaku Number. Instead, you should say that you don't have a Shusaku Number.
unkx80: I thought it makes sense. And it is actually used in things like a distance matrix for a graph: if the edge (i, j) does not exist in the graph, then the (i, j)-entry in its distance matrix is infinity, or sometimes written as a big M instead.
Bildstein: I think it only makes sense in the intuitive sense that if you don't have a Shusaku Number then yours could be considered higher than everyone elses, and the only number higher than every other number is infinity. That seems like a bit of a stretch to me. And it makes non-sense for other, more tangable, reasons, as I described above.
Also, I don't see why we should be influenced by the lanugage of mathematics. Often mathematicians use infinity to represent concepts that don't really mean something like "really, really big", but rather as a device for communicating another quality of standing apart from the rest of a set. I see your graph-theory example as an example of this. In the graph theory case, I think it makes more sense to arbitrarily call the 'distance' 'M' than infinity, because there is no connection between the two vertices. There is not actually some connection that is infinitely long.
ilan: Here is one reason for defining your Shusaku number to be infinite if there is no sequence linking you to him: As the Shusaku number grows, it is reasonable to say that you are less linked to Shusaku. The minimal possible link occurs when there is no sequence of games linking you to him, which, by the previous sentence, means that your Shusaku number if it exists, must be greater than any Shusaku number generated by an actual sequence of games, so greater than any positive integer, therefore infinite.
This argument uses the principle that if one is forced [3] to define something which doesn't actually exist, one can still do this by using partial information. Here is another example: The symbol 1/0 is generally regarded as undefined. However, it still retains some properties. In particular, it is true that 1/(1/0) = 0, in the sense that no matter what you mean by 1/0, that equation will hold. You should see that this example is essentially the same one as in the previous paragraph.
Tom: It seems sensible [3] to me to extend the straightforward definition of Shusaku number to this: it is the greatest element of the set {0,1,2,...,infinity} which is not greater than the size of some linking game set.
[3]Bildstein: Sure. You're both talking about the intuitive sense that I talked about earlier. But it's only intuitive because of you understanding of mathematics and infinity. But this is not a purely mathematical problem, we're talking about something with real meaning, that should be meaningful to people without an understanding of mathematics. For this reason, I think we should define someone who doesn't have a finite Shusaku Number as not having a Shusaku Number.
ilan: I think you're basically right. My above argument merely says that if a Shusaku must be assigned to someone who doesn't have one, then it must be infinity.
Bildstein: Yes, I would certainly agree with that.